Abstract
The proofs of generalized Hardy, Copson, Bennett, Leindler-type, and Levinson integral inequalities are revisited. It is contemplated to establish new proof of these classical inequalities using probability density function. New integral inequalities of Hardy-type involving the r th order Generalized Riemann–Liouville, Generalized Weyl, Erdelyi–Kober, (k, ν)-Riemann–Liouville, and (k, ν)-Weyl fractional integrals are established through a probabilistic approach. The Kullback–Leibler inequality has been applied to compute the best possible constant factor associated with each of these inequalities.
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